## Stream: maths

### Topic: name help

#### Johan Commelin (Jun 04 2020 at 09:30):

Given an R-algebra homomorphism mv_polynomial I R →_a[R] mv_polynomial J R, you get an induced function (J → R) → (I → R). What is a good name for this? It is a sort of "Spec functor for dummies".

#### Johan Commelin (Jun 04 2020 at 09:30):

Should this just be mv_polynomial.comap?

#### Johan Commelin (Jun 04 2020 at 09:55):

Yup, I think it should be comap. Thanks for rubberducking!

#### Chris Hughes (Jun 04 2020 at 10:16):

I don't understand why it is comap. Usually comap is the map on homsets for contravariant functors.

#### Johan Commelin (Jun 04 2020 at 10:26):

It's contravariant in the index set of the variables.

#### Chris Hughes (Jun 04 2020 at 10:39):

What's the functor?

#### Chris Hughes (Jun 04 2020 at 10:39):

I guess it's a natural transformation

#### Johan Commelin (Jun 04 2020 at 10:58):

Normally, you have a functor from R-algebras to affine schemes over Spec(R). If R is an integral domain, there is a natural map from I → R to the spectrum of mv_polynomial I R, that sends a point x to the kernel of aeval _ _ x.

#### Johan Commelin (Jun 04 2020 at 10:58):

The spec functor is contravariant. And this comap thing is a silly approximation to Spec.

#### Johan Commelin (Jun 04 2020 at 10:58):

(It's not even getting close.)

#### Johan Commelin (Jun 04 2020 at 10:59):

But other suggestion for a name are very welcome!

#### Chris Hughes (Jun 04 2020 at 11:23):

In my mind, mv_polynomial.comap means mv_polynomial is a contravariant functor. I can't think of a better name.

#### Johan Commelin (Jun 04 2020 at 11:27):

Yeah, I agree that the name is not optimal

#### Kevin Buzzard (Jun 04 2020 at 14:00):

Maybe it's a bit like ext where there is sometimes more than one contender

Last updated: May 14 2021 at 19:21 UTC